Controlling Fusion of Majorana Fermions in one-dimensional systems by Zeeman Field

TL;DR

This paper proposes a method to control Majorana fermions in a 2D topological insulator edge using a Zeeman field, enabling their manipulation and detection through topological phase transitions.

Contribution

It introduces a novel approach to manipulate Majorana fermions via Zeeman field variations in a 2D topological insulator system.

Findings

Majorana fermions appear at junctions with transverse exchange field h.

Reversing h permutes the Majorana fermions.

Decreasing h can fuse Majorana fermions into Dirac fermions, indicating a topological phase transition.

Abstract

We propose to realize Majorana fermions (MFs) on an edge of a two-dimensional topological insulator in the proximity with s-wave superconductors and in the presence of transverse exchange field h. It is shown that there appear a pair of MFs localized at two junctions and that a reverse in direction of h can lead to permutation of two MFs. With decreasing h, the MF states can either be fused or form one Dirac fermion on the {\pi}-junctions, exhibiting a topological phase transition. This characteristic can be used to detect physical states of MFs when they are transformed into Dirac fermions localized on the {\pi}-junction. A condition of decoupling two MFs is also given.